A parallel-acting iterative automaton

deterministic automata are defined in an attempt to capture the essential features of an iterative one-dimensional array of finite-state machines operating under the direction of a central control where at discrete time steps each machine in the chain is receiving the same instruction as each of the other machines. Each machine in the array is also capable of direct communication only with immediately neighboring machines. Some general theory is developed, and the sets of strings definable by these automata are described.